Using one tablespoon of the butter, rub it all over the inside of an 8x8" casserole dish- bottom and sides. Set aside.
Add the rest of the butter to a large skillet and set it over medium high heat. As soon as the butter's melted reduce the heat to medium. Add the onions and pepper, stirring to combine. Cook for 3-4 minutes, stirring often, just until the vegetables begin to soften.
Add the garlic, tomatoes, and broth to the skillet. Stir everything together to evenly combine. Turn the heat to high, and bring the mixture to a boil.
Slowly pour the grits into the skillet, stirring constantly to incorporate, until they're all evenly combined. Continue stirring until the mixture come back to a boil, then immediately reduce the heat to low.
Let the grits simmer for 5-6 minutes, stirring often. Remove the skillet from heat. Carefully (mixture will be HOT), season with salt and pepper to taste.
Add the egg, stirring in quickly so that it evenly combines before it begins cooking. Add the shrimp, bacon, and one cup of cheese- stir together until evenly incorporated.
Transfer the grits mixture to the prepared casserole dish, and spread it out evenly with a spatula. Sprinkle the remaining cheese evenly out overtop.
Bake the casserole at 375° for 30 minutes, or until the casserole's hot and bubbling with melted cheese on top.
Carefully remove the hot dish from the oven, and let it rest for 5-10 minutes before serving.